Well, as long as you understand it!

If the order is important, it'd be interesting to have two identical cars, power mileage, service history etc., and to do the oil and engine restorations in opposite orders and see what falls out (I'd predict that doing the oil first gives a 5% higher power in the "in-between" stage than doing the engine restore first).

To me, though, a *5%* (*5/100*) maximum loss of overall engine power due to oil deterioration implies multiplying the "base" horsepower (including any engine deterioration, or high mileage deterioration - *5%* is a relative measure) by *0.95*, i.e. *1 - 0.05 *or* (100 - 5) / 100.*

Note that the inverse process, dividing *1401* by *0.95*, yields *1475* also. *1401* is not the base power, it is the oil-deteriorated power. Now: *1401 * 1.05* is only *1471* ish - that is not the correct inverse function in this case, and gives an error of over *5%* in the increase i.e. *4/74*, as stated.

The same applies to the engine deterioration: *1549 / 0.95 = 1630* (ignoring rounding issues and going by the numbers the game gave you).

It just makes more sense to me that the engine power modifications would be applied multiplicatively, and compoundly, e.g. as in the following potential candidate for the "governing equation":

C*urrentHp = stockBrandNewHp * oilFactor * engineFactor * mileageFactor*

*oilFactor* exists in the range *0.95* to *1.05*.

*engineFactor* in the range *0.95* to *1.00*.

*mileageFactor* in the range *1.00* or lower (to some unknown limit, if present).

So in the case of oil, engine and ignoring the mileage deterioration, we have:

*1401 = stockBrandNewHp * 0.95 * 0.95 * mileageFactor*

Where *stockBrandNewHp* and *mileageFactor* are constants for our purposes here, and their product can be represented as *P*.

i.e.:

*1401 = 0.95 * 0.95 * P*

After the oil change:

*1549 = 1.05 * 0.95 * P*

After the engine restore:

*1630 = 1.05 * 1.00 * P*

We can verify this representation accordingly by doing the calculations:

*1.05 * 1401 / 0.95 = 1549*

1.00 * 1549 / 0.95 = 1630

Or by noting that *P* should be constant in each line:

*P = 1401 / (0.95 * 0.95) = 1401 / 0.9025 = 1552*

P = 1549 / (1.05 * 0.95) = 1549 / 0.9975 = 1552

P = 1630 / (1.05 * 1.00) = 1630 / 1.0500 = 1552

The stock un-boosted power was *1556 hp*, so the mileage factor would appear to be about *0.9975* at this point. That's about *2.6%* per *100 000 km*, which is close to the value you suggest: *(19 568.3 - 10 000) / 100 000 * 2.6% = 0.25%* decrease, or *99.75%* of the initial. Using more precision in the calculation, i.e. 0.997429..., yields *2.7%*. The more miles someone puts on a car, the more accurate we can be (and I appreciate the great effort in that regard.)

The hp rounding issue is massive here: if the power were actually *1551*, that would be *3.4%* per *100 000 km*; *1553* and it's only *2.0%* per *100 000* km.

Somewhere between two and four percent seems certain - that could be narrowed further by looking at other points in your data. **Edit**: actually, it's between about *2.35* and *3%*, because "*1552*" is at minimum *1551.5* and at most *1552.49*... But looking at more numbers will still help.

What's interesting is that it doesn't appear that you're wrong overall (I used your first post to define the "equation" I just tested), just that you might be attributing actual hp value changes in the wrong proportion to each effect, or that you're just summing things differently from the way I see it. It's clear that we need to be working in relative differences rather than absolute horsepower differences.

But I appreciate I could still just be being thick!

Last edited: Feb 22, 2014